The Total Amount Of Possible Gear Permutations

(Disclaimer: I am dumb at math so I’ll be taking criticism and help from u guys to correct this)
This thread is dedicated to find the total amount of POSSIBLE gear permutations which takes skillpoints into one of the factors which makes all these builds ingame usable(Ofcourse I wont list all the builds since it would be tedious and thread would be too big) I have only tried to do this by myself so expect alot of mistakes!

Sources:
Wynndata (For the amount of items)
Myself

Spoiler: Amount of items:

Armour:
Helmet-369
Chestplate-346
Leggings-323
Boots-329

Accessories:
Ring-226
Ring-226
Bracelet-180
Necklace-175

Weapons:
Dagger-328
Wand-325
Bow-328
Spear-329
Relik-280

Sum of all armours and accessories:
2174

Spoiler: Formulas Used

Permutation Formula: n!/(n-r)!
Fermi Estimation: multiply by 0.00001 (This one is a large bad assumption from me which I could really appreciate if someone could help correct this one)

Spoiler: Process

1.Add all amounts armor and accessories and save and refer to this value as (n)
2.Add the amount of one of the types of weapon to (n) and then run it through the formula for permutations with a sample size of 9 (r).
3.Do this for all the weapons and store these values in a notepad somewhere.
4.After doing this sum up all the values you have and it should round up to 1.83026108083391e+31.
5.However, this isnt the final answer yet as skillpoints matter and we want this to be somewhat realistic because of skill points limitations so what I used was fermi estimation to find the estimated amount of possible permutations of gears and the result should be 1.83026108083391e+26

Spoiler: Conclusion

The result is somewhat misleading(by a couple million or more) as we just used an estimation method and not an actual precise method(which would take weeks) but my result which is 1.83026108083391e+26 should be close enough to the real answer.

Edit:
Another answer (a more realistic one) has been posted thanks to forum user Robbee it should be somewhere near 1.74e+21! the full explanation as to why can be found in the first page of the thread.

Any comment and help to correct this would be appreciated ^^

 

wow.
I didnt think somebody would do something like that

 

fuck class building lets just list every single possible build and pick our favourites from there
what if you also included every single possible id roll combination

 

Im assuming this is not taking Hive items into account (though I guess multiple hive are still "wearable" just not practical)

 

Most of those builds wouldn’t work due to having too many sp requirements.

 

one of them is the most optimal build and we must find it

 

Wynncraft Challenge: Roll a random number between 1 and 1.83026108083391e+26 and play the game until you have the set

 

Wearing multiple items from the same division is not tight on sp. They are literally the same element.

 

They give a massive penalty.

 

In this case, you can't use the permutation formula, because this would allow builds consisting of 9 helmets, for example. The actual formula should look like this:

369 * 346 * 323 * 329 * (226 * 225 / 2 + 226) * 180 * 175 * (328 + 325 + 328 + 329 + 280) = 1.743062116e+22

For your helmet, you have 369 possibilities. For each of these 369 options, you can again choose between 346 chestplates, which results in 369 * 346 combinations. And so on.
Rings are a bit different, as the order in which they are chosen doesn't matter, Prism + Intensity and Intensity + Prism are basically the same build. So for your first ring you have 226 options, which leaves 225 options for the second ring, if they are supposed to be different. Divide by 2 because of symmetry and add 226 combinations for having the same ring twice. Note that you cannot calculate 226 * 226 / 2, as each combination of two identical rings can only be hit once, so the /2 shouldn't apply to them.

However, this is still without skill points taken into consideration, but I would actually assume that most builds are feasible. Remember that most items are for lower levels and have therefore low skill requirements. If you go to wynndata and sort items by their strength requirement, only about half of the displayed 500 items require at least 40 strength, which is the average amount of sp available for each element (without bonus sp from ids). Which means that the probability to require more than 40 strength for a random build is only about 1 - (1 - 250 / 3764)^9 = 46.127%. And thats only one element out of five. Of course you cant just use 0.46^5 to calculate the chance for a build to be infeasible, this is just to demonstrate how "rare" high skill requirements are, which means that 1.74e+22 should be relatively close to the actual number.

 

You are late to the party read the previous comments sorry

 

First of all, thanks for the feedback! I didn’t really put much thought into what I posted. I will edit the post with the new answer and also give credits to you! It seems that I have also mixed up permutation and combination since permutation by definition is the one where order matters while in combination order does not and I just quickly assumed that it was permutation because order mattered.

 

Well, in this case it isn't really about permutation vs combination, as you don't have a single pool of items to draw from, instead you have a different pool for each slot. If you would have to draw nine items from a single pool, your thought process would be right, but in this case, you draw one item (or two for rings) from eight pools and combine them through multiplication.
But I'm glad that I could help!